Abstract
In eigenvalue problems for the Orr-Sommerfeld equation with nonclassical boundary conditions (which differ from the adhesion conditions), the applicability of the Squire transformation is studied (this transformation enables one to reduce the three-dimensional picture of perturbations to the two-dimensional picture in the plane of the principal shear. Linearized equations are derived that generalize the Orr-Sommerfeld equations to tensor linear non-Newtonian media. It is shown that the Squire transformation algorithm is not applicable to stability problems for shear flows of these media.
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Georgievskii, D.V. Applicability of the squire transformation in linearized problems on shear stability. Russ. J. Math. Phys. 16, 478–483 (2009). https://doi.org/10.1134/S1061920809040025
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DOI: https://doi.org/10.1134/S1061920809040025